@article{amp2017513,
author={Evako, Alexander V.},
title={Graph Theoretical Models of Closed n-Dimensional Manifolds: Digital Models of a Moebius Strip, a Projective Plane a Klein Bottle and n-Dimensional Spheres},
journal={Applied Mathematics and Physics},
volume={5},
number={1},
pages={19--27},
year={2017},
url={http://pubs.sciepub.com/amp/5/1/3},
issn={2333-4886},
abstract={This paper presents discretization schemes for building graph theoretical models of n-dimensional continuous objects with the same topological properties as their continuous counterparts. An LCL collection of n-cells in Euclidean space is introduced and investigated. The digital model of a continuous n-dimensional object is the intersection graph of an LCL cover of the object. We prove that the digital model of a continuous closed n-dimensional manifold is a digital closed n-dimensional manifold. It is shown that the digital model of a continuous n-dimensional sphere is a digital n-sphere with at least 2n+2 points, the digital model of a continuous projective plane is a digital projective plane with at least eleven points and the digital model of a continuous Klein bottle is the digital Klein bottle with at least sixteen points.},
doi={10.12691/amp-5-1-3}
publisher={Science and Education Publishing}
}